This guidance confirms this is the case: https://www.dgc.gov.it/web/faq.html#:~:text=In%20quanto%20tempo%20viene%20generata%20e%20per%20quanto%20tempo%20%C3%A8%20valida%20la%20Certificazione%3F73
We've emailed our resort our son's vaccine record from our GP for his 1st dose plus this guidance, waiting to hear back. Will update once I do